The Bible say: "And after six days Jesus taketh Peter, James, and John his brother, and bringeth them up into an high mountain apart," Matthew wasn't here. Then, Why Matthew describe with details that event? The answer we can find in Luke 1: "Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us, Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word" He wrote the things that the eyewitnesses told him.